She was born Joan Marie McInroy in Topeka, Kansas, the daughter of Leonard and Mary Sands McInroy. She graduated from high school in Manhattan, Kansas in 1942. In 1957, she married Spencer Finney, Jr. and had three children, Sarah "Sally" Finney Timm, Richard Finney, and Mary Finney Holladay. In 1978, she graduated from Washburn University with a degree in economic history. From 1953 to 1969, she served on the staff of Republican U.S. Senator Frank Carlson. From 1970 to 1972, she served as Commissioner of Elections for Shawnee County, Kansas. In 1972, running as a Republican, she was an unsuccessful candidate for a U.S. House seat in Kansas's 2nd congressional district. She also served as a Special Assistant to Topeka Mayor Bill McCormick.[1]

After switching her political affiliation from Republican to Democrat, she served as the first female Kansas State Treasurer from 1975 to 1991. Her staff her first term as Treasurer included Nancy Claggett and Kathleen Boston Cole McCune as Deputies. After upsetting former Governor John W. Carlin in the 1990 Democratic primary for Governor, she defeated incumbent Republican Mike Hayden in the general election becoming the first woman to defeat an incumbent Governor in a general election in the United States.

In addition to being the State of Kansas's first female governor, she was Kansas' oldest governor, taking office at age 65, Kansas' first Roman Catholic Governor, and also one of the few pro-life Democratic Governors of her time[2]

Following her term as Governor, in 1996, she ran for the U.S. Senate seat vacated by Bob Dole, but was defeated in the Democratic primary by Jill Docking, who gained 75% of the primary vote, who later lost the general election to Sam Brownback.

She died in 2001 from complications of liver cancer at the St Francis Hospital and Medical Center, Topeka, and is buried in Mount Calvary Cemetery in Topeka.[1]